Recent advances in data-driven modeling approaches have proven highly successful in a wide range of fields in science and engineering. In this talk, I will present our weak form methodology which has proven to have surprising performance and robustness properties. In particular, I will describe our equation learning (WSINDy) method and illustrate application to learning interaction potentials and mean field limits for interacting particle systems. I will also discuss how our approach offers advantages in terms of computational efficiency, noise robustness, and modest data needs.